Make Summer Practice Fun With Games!

Congratulations! You are in the final stretch of the school year. Teachers, students, and parents are feeling excited about the carefree summer months ahead and potentially anxious about keeping students’ math skills fresh.

You will inevitably receive inquiries from parents asking how they can help their children over break.

When given the choice, rarely will a child choose to do paper-pencil workbook work over playing a game. These student-approved games require minimal materials and are easy to play at home.  They promote number sense and fluency and, as an added bonus, kids love to play them!

What should students practice?

Following is a list of skills to practice for Kindergarten through 3rd grade. Because the skills build, a student should practice the skills from the grade level just completed and the grade level below. Students in 4th grade and above would also benefit from practicing all the skills listed.

  • Kindergarten: Number combinations to make 10
  • First Grade: Recall from memory addition and subtraction within 20, addition and subtraction within and up to 100 using mental math strategies.
  • Second Grade: Recall from memory multiplication and division facts for 2, 3, 4, 5 and 10.
  • Third Grade: Recall from memory multiplication and division facts for 6, 7, 8 and 9, 2-digit by 1-digit multiplication, division of a 2-digit number by a 1-digit number

What should parents have on hand to make math fun over the summer?

All you need to play the games below is a deck of cards! (Dice are good, too.)

What could students play?

Here are three of our favorite games.  All can be adapted to practice across grade levels.


Number of players: 2 (more for a challenge)
Materials: None
This game resembles Rock-Paper-Scissors.  When players say “Math!” each shoots out 1-5 fingers on one hand. The first player to find the sum of both
their fingers and their partner’s fingers wins the round. For example, I shoot out 3 fingers and my partner shoots out 5 fingers. The first to say 8 wins.


  • Use both hands to add up to 20
  • Use one hand and multiply the fingers for facts up to 5 x 5. For example, I shoot out 3 fingers and my partner shoots out 5 fingers. The first to say 15 wins.
  • Use 2 hands and multiply for facts up to 10 x 10.
  • Play with more players to add or multiply multiple numbers for a challenge


Number of players: 3 (more for a challenge)
Materials: Deck of cards with face cards removed, ace is 1
Split the deck in half and give each pile to 2 of the players. The third player is the Caller.  When the Caller says, “Salute!” the players each flip a card from their pile and place it on their forehead to salute each other.  Each player can see the others card, but not their own. The Caller tells them the sum of the 2 players cards. The first player to tell the number of their own card wins the round. Players can switch jobs after each round or when the pile of cards is depleted.


  • The Caller tells the product of the 2 players cards.
  • With 4 players (one Caller and 3 players) students can practice sums or products of 3 numbers.
  • Need more challenge? In the picture, the Caller has squared our numbers before adding them together and Melanie and Cassy are trying to find their own number.

Greatest Sum!

Players: 2 or more
Material: Deck of cards with face cards and 10 removed, ace is 1

This game is played like the card game of War. Shuffle the deck and place it in the center.  Each player chooses 2 cards off the top of the deck and finds the sum of their cards. The player with the greatest sum wins the cards for the round. Play continues until the deck is depleted or until time is called. This game is great for practicing mental math strategies, but can also be used to practice traditional algorithms with paper and pencil (see the variations).


  • Players choose 2 cards and find the difference. The player with the smallest difference wins.
  • Players choose 2 cards and find the product. Greatest product wins.
  • Each player chooses 3 cards and creates a 2-digit and a 1-digit number and finds the sum or difference. The player with the greatest sum or least difference is the winner.
  • Each player chooses 3 cards and creates a 2-digit and a 1-digit number and finds the product. The player with the greatest product is the winner.
  • Each player chooses 3 cards and creates a 2-digit and a 1-digit number and finds the quotient and remainder when the 2-digit number is divided by the 1-digit number. The player with the greatest remainder wins.
  • Each player chooses 4 cards and creates two 2-digit numbers and finds the sum or difference. The player with the greatest sum or least difference in the winner.

Adding the element of competition to practicing basic facts makes it more fun for all. Let us know if you have a favorite game you’d like to share.

Looking for more ideas? See: “Summer Math” Suggestions to Boost Student Understanding”


Mantra for 2017: Make math make sense!

The return from winter break brings with it a refreshed outlook on teaching.  Teachers return with an eagerness and enthusiasm for the profession and students return seeming just a little more mature.

Return from winter break also brings with it a sense of urgency.  Maybe you’re not as far along in the curriculum as you had hoped. You realize that the frantic push to cover material before break has left students unable to recall content taught.  You are feeling the pressure of standardized tests looming.

The 2015 TIMSS results were recently published and once again, Eastern Asian countries top the charts.  In fact, the gap between the top 5 scoring countries and the United States was 54 points.  What sets them apart is their commitment to teaching mathematics at a deep conceptual level with a focus on thinking and problem-solving.

All of that can be very sobering.  Take a deep breath and set some goals.

Ask more, tell less

  • How do you know that’s correct?
  • Are you sure?
  • Why does it make sense?
  • I wonder why that works.
  • Can you solve it in another way?
  • Can you build or draw a representation?
  • What do you see in your head?
  • Can you prove your answer is correct?
  • You and your neighbor have different answers, who is correct?

Allow time for understanding

It’s easy this time of year to get caught up in the pressure to cover content, but remind yourself that memorization is not the end goal, understanding is.  Taking the time to focus on the concrete-representation-abstract approach will ultimately lead to deep conceptual understanding.  Your students (and their test scores) will reap the benefits.

Help students make connections

  • How is this like what we just learned?
  • Does this remind you of anything?
  • Can you make a connection between this and what we have already learned?

By setting a few simple goals, you will set yourself and students up for a successful remainder of the year!


Mental Math Breaks

rock paper scissorsTo make the most of the upcoming weeks, try taking some mental math breaks.

These few weeks between Thanksgiving and winter break can arguably be the most challenging weeks to keep on pace with curriculum and keep students engaged.  With the anticipation of the holidays and a much-needed winter break on students’ minds, they can quickly lose focus.  Now more than ever, you will find the need to give your students mental breaks in the day.  So, why not practice a little math?

The following games can be practiced just about any time and anywhere if you have a few simple materials on hand.

Make Ten

Skills Practiced: Sums to 10, 20 or 100

Materials: Number cards 0-10, 2 of each or enough for as many pairs as you will need for your class

Pass out 1 number card to each student face down.  When you give the signal to go, students cycle around the room to find another student with a card whose number when added to their own makes ten.  Once they have found their partner, both students sit down.  You can reshuffle the cards and play multiple rounds.  Set a timer for each round and challenge your students to beat the fastest time recorded.

Variations:  Program the cards to make 20 or 100


Skills Practiced: Addition and Multiplication facts

Materials: none

The game is played like Rock-Paper-Scissors except when students say, “MATH!” each student shows 0-5 fingers on one hand.  The first student to say the sum of their fingers and their partners fingers combined wins the round. Students can play best 2 out of 3 with one partner and then rotate around the room to find a new partner and continue to play until time is up.

Variations: Find the product of the two sets of fingers or use both hands to find the sum or product.

Ping! Beep! Ping-Beep!

Skills Practiced: skip counting, multiples and common multiples

Have the class stand.  Choose a target number. Let’s use 4 for our example.  Begin by having students count off, starting with one.  Instead of saying the number, the student that would say 4 says “Ping”.  As the count continues, for every multiple of 4, students say, “Ping”.  Every time a mistake is made, the count starts over.

For more of a challenge, choose 2 target numbers.  Let’s use 4 and 5 for our example.  Begin at one.  For every multiple of 4 or 5, students say “Ping” and for every common multiple of 4 and 5, like 20 students say “Ping-Beep”.  The count starts over with every mistake made.

Challenge your students to beat the count from previous rounds.

Keep your students focused with these movement games and practice some mental math at the same time!


Journaling in the Singapore Math Classroom

Communicating mathematically is a critical skill and goal for all of our students to reach by the end of middle school. In fact, Common Core Standards for Mathematical Practices, MP3, states that students will, “Construct viable arguments and critique the reasoning of other.”

Singapore’s Ministry of Education would tell you that there’s nothing Singaporean about Singapore math.  When developing their highly successful math curriculum, they took theory and ideas from mathematicians and educational theorists around the world and put them into action.

What should a math journal look like?

I have attended many workshops and make-and-take sessions on planning and preparing for student math journals.  Many have focused on setting up the student journal with a contents page and tabs to divide the journal into “notes,” “vocabulary” and “practice problem” sections.  While this will create a journal that looks really nice, what I have found to be most effective (and one that I actually use in the classroom) is taking a simple composition or spiral bound notebook and beginning on the first page.  Students make their first journal entry of the school year on page one and continue with entries on subsequent pages. Less is more!

Here’s what a journal entry page might look like:


The journal entry number just grows as the year progresses.  We might come up with the title as a class, or students can create their own.  The problem in the problem box can be copied by students or printed out for students to paste in their journals.

What should students put into journals?

There are four basic types of journal entries; investigative, descriptive, evaluative and creative.

Investigative: Students explore a new concept, solve a problem and make connections to prior learning.

  • Example: Three friends share a sleeve of cookies.  Each sleeve holds 32 cookies.  If each friend eats ¼ of the sleeve, how many cookies do they eat altogether?

Descriptive: Students describe or explain a concept or mathematical vocabulary.

  • Example: Use pictures, numbers and/or words to explain a polygon.

Evaluative: Students argue for or against a strategy or solution to explain why they think an answer is right or wrong, explain their choice of strategies or justify the most efficient strategy.

  • Example: Which of the strategies discussed in class today would you use to solve 245 – 97?  Why?

Creative: Students write their own word problem or create their own number puzzle.

  • Example:  The answer is 465 lbs.  What’s the question?

Here’s a sample student  journal page (click on image to enlarge):


When should I ask students to make journal entries?

Journaling can be a very effective tool to develop communication skills in your students.  Depending on the type of entry, you could incorporate journaling into many parts of your math day.  Open a class with an investigative entry to engage students.  Consolidate learning and reflect on thinking with a mid-lesson descriptive or evaluative entry.  Enrich students with a creative entry for early finishers of independent practice.

The benefit of journaling for the teacher is it provides a concrete formative assessment.  By evaluating student responses, you can determine their readiness to handle a new task and check for understanding of concepts.  Student journals also provide a great launching point for discussion at parent-teacher conferences.


Check out a resource from a previous post: Singapore Math and Math Journal Writing


“Summer Math” Suggestions to Boost Student Understanding

School is out and summer is calling, but for many teachers and administrators, summer is a time to take stock and plan and budget for next year.

As a teacher, this is a glorious time of year, but also one of worry. I worry about my students.  I worry about those who needed extra support throughout the year understanding and retaining math concepts.  How will they fare next school year? Will they regress over the summer months if they don’t do any math work?

There are three categories of students who benefit most from summer math work:

  • Those who have struggled all year and maybe never quite achieved mastery on those critical grade level concepts,
  • those who easily forget concepts, and
  • those whose math confidence could use a boost.

With a Singapore Math program, there aren’t many ready-made options to pick up at the local bookstore.  Books that are  available focus heavily on procedural understanding rather than underlying math concepts. So what’s a teacher to do?

Aside from recommending tutoring, I have found a couple of options that seem to meet my needs as a teacher and the needs of my students.

Workbook Work

Primary Mathematics Common Core Extra Prac 3

For those looking for a paper and pencil option, I recommend the Extra Practice books from Singapore Math’s Primary Mathematics series. Students should work at the grade level just completed (a rising 3rd-grade student should do summer work in the 2nd grade Extra Practice book).

The Extra Practice books offer parents and/or tutors “Friendly Notes” at the beginning of each unit that explain how to re-teach concepts in a way that is familiar to the student.  The notes are followed by practice pages that give parents sample problems appropriate for practicing the concepts and the student an option of working through problems independently.  Best of all, they include an answer key in the back so parents can check work and students can re-work problems, if necessary.

These books are written to cover a year’s worth of concepts; I am by no means suggesting that a child complete the entire book over the summer.  Teachers recommending this book will need to tailor the tasks to meet each student’s needs.  This can be as simple as highlighting the contents page to include units or pages that you would like the student to complete over the summer keeping those critical concepts in mind.

Another option for summer work can be found in online programs.  I have come across three online options for concept practice; Primary Math Digital, it’s twin Math Buddies and a program new to the US market, Matholia.

Online Options

Primary_Digital_Coming_Soon_Home_SchoolPrimary Math Digital (Free 15-day trial) and Math Buddies (Also a free trial) are backed by Singapore Math’s Primary Mathematics and Math in Focus series. Both offer students video tutorials that can be viewed by the student (and parent) an unlimited number of times.  These videos are scaffolded to follow the pictorial and abstract progression of learning.

Teachers can assign videos, practice and assessment tasks fMath Buddiesor students to complete over the summer at their own pace.  The practice pages can be a little challenging to navigate, but with some initial guidance, students should be able to complete the tasks independently.

Both programs require the school to purchase annual student and/or teacher accounts to gain access to the library of lessons. There are Homeschool accounts available. Expect a price tag of around $30 per student depending on the number of accounts purchased.

matholia logoAnother, more affordable option new to the US market is Matholia. Matholia was developed by two teachers from Singapore and has been used by teachers and students in Singapore as well as several other countries. This program also includes a library of video tutorials, practice and assessment tasks as well as fact fluency tasks and games.

The videos are easy to understand and are also strategically scaffolded for student understanding. The practice and assessment tasks are intuitive and easy for students to navigate. As with the other programs, teachers can assign tasks for students to complete over the summer.

Matholia also requires the school to purchase annual student accounts (teacher accounts are free) but is much more affordable at just $8 per student.

Don’t forget the concrete…

I can’t go without saying that any of these options will give students practice, but struggling students need more than just extra practice working through math problems.  They need more time in the concrete phase of learning using manipulatives; base-ten blocks, place value chips, model building with connecting cubes or paper strips, fraction strips or circles, etc.  So, please, consider not only sending these students home with books and login IDs but also with a bag of manipulatives for hands-on learning and practice.

Beach_of_Dreams_BeautifulNow…back to dreams of lazy mornings and time to relax and recharge.  Have a great summer and rest assured that your students will be prepared for the next grade with a little summer math work.